Cock (software)

Coq is a Assistant of proof developed with INRIA, the Polytechnic school and the Université of Paris XI (and before with the National university of Lyon) within the framework of the LogiCal project ().

Cock is based on the Calcul of constructions (introduced by Thierry Coquand, CoC shortened in English, from where a word game justifying the name of the system), a Théorie of the types of higher Ordre, and its language of specification is thus a form of typified Lambda-calculation. The calculation of constructions used in Coq includes/understands inductive constructions directly, from where its name of calculation of inductive constructions (CIC).

Cock was recently equipped with increasing functionalities of automation. Let us quote in particular the tactics Omega which decide the Arithmétique of Presburger.

More particularly, Coq allows:

to handle assertions of calculation;
mechanically to check evidence of these assertions;
to help in the search of formal evidences;
to synthesize programs certified starting from constructive evidence of their specifications.

It is a Free software distributed according to the terms of the license GNU LGPL.

Among great successes of Cock, one can quote the completely mechanized demonstration of the Théorème of the four colors by Georges Gonthier and Benjamin Werner.

See too

the site of the project

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